Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 824: 36

Answer

See below.

Work Step by Step

An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. If it exists, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here $|0.25x|\lt1\\-1\lt 0.25x\lt 1\\-4\lt x\lt 4$. Hence the sum: $\dfrac{6}{1-0.25x}$
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